Owing to the wide separation of the natural frequency of the sprung parts from that of the unsprung parts, the bounce and pitch motions of the vehicle body and the wheel motions exist independently. The sprung parts of a vehicle weigh 98 kN, its center of gravity is 108 cm behind the front axle and the wheelbase is 230 cm The combined stiffness of the springs of the front suspension is 25 kN/m and that of the rear suspension is 27 kN/m. The radius of gyration of the sprung parts about a horizontal transverse axis through the center of gravity is 0.92 m.
a) Calculate the natural frequencies of pitch and bounce motions of the vehicle body. Also determine the location of the oscillation centers.
b) If the radius of gyration of the sprung parts of the vehicle can be varied, determine the conditions under which the oscillation centers of the vehicle body will be located at the points of attachment of the front and rear springs. Also calculate the natural frequencies of the sprung parts.